Grothendieck´s section conjecture predicts that the rational points on curves over finitely generated fields are determined by maps between etale fundamental groups. Over R, this conjecture becomes the prediction that pi_0 applied to the natural map from the fixed points to the homotopy fixed points of a real curve with its Z/2 action provided by complex conjugation is a bijection, which follows from Sullivan´s conjecture, proven by Haynes Miller and Gunnar Carlsson. We show a 2-nilpotent section conjecture over R: for a curve X over R such that each component of its normalization has real points, pi_0(X(R)) is determined by the maximal 2-nilpotent quotient of the fundamental group with its Z/2 action. This implies that the set of real points equipped with a real tangent direction of a smooth compact curve X is determined by the maximal 2-nilpotent quotient of the absolute Galois group of the function field, showing a 2-nilpotent birational real section conjecture.